Statistical inference consists of estimating parameters and testing hypotheses. Estimation has already been discussed, so this portion is about testing hypotheses. Point estimation and interval estimation, as discussed earlier, have their own fields of application.
Sometimes there is a situation in which the point estimation and the interval estimation are either not required or the estimation of parameters does not provide any inference. For example, the following situations require inference, which is not possible by methods of estimation:
- The ingredients of a medication have been changed to improve its effectiveness. In this situation both the point estimation and the interval estimation fail to answer the question about the improvement of the medicine. In this case we have to get help from the sample data to decide whether or not the medicine has been improved.
- A tire manufacturer claims that the average life of their tires is at least 15000 kilometers. The life of tires is an important factor to determine the price of the tires. It is significant if we prove with a reasonable amount of confidence that the life of the tires is not more than 15000 kilometers. The answer is not provided by a point estimate or by an interval estimate of the life of the tires. We shall examine the claim of the manufacturer on the basis of an experiment conducted on a sample of tires, and a certain procedure will be adopted to reach a conclusion. This is what we shall call the test of the hypothesis about the life of tires.